Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In this paper, we study the family of GGMs with small feedback vertex sets (FVSs), where an FVS is a set of nodes whose removal breaks all the cycles. Exact inference such as computing the marginal distributions and the partition function has complexity $O(k^{2}n)$ using message-passing algorithms, where k is the size of the FVS, and n is the total number of nodes. We propose efficient structure learning algorithms for two cases: 1) All nodes are observed, which is useful in modeling social or flight networks where the FVS nodes often correspond to a small number of high-degree nodes, or hubs, while the rest of the networks is modeled by a tree. Regardless of the maximum degree, without knowing the full graph structure, we can exactly compute the maximum likelihood estimate in $O(kn^2+n^2\log n)$ if the FVS is known or in polynomial time if the FVS is unknown but has bounded size. 2) The FVS nodes are latent variables, where structure learning is equivalent to decomposing a inverse covariance matrix (exactly or approximately) into the sum of a tree-structured matrix and a low-rank matrix. By incorporating efficient inference into the learning steps, we can obtain a learning algorithm using alternating low-rank correction with complexity $O(kn^{2}+n^{2}\log n)$ per iteration. We also perform experiments using both synthetic data as well as real data of flight delays to demonstrate the modeling capacity with FVSs of various sizes.

We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with unknown cluster patterns. Specifically, a pattern-coupled hierarchical Gaussian prior model is introduced to characterize the statistical dependencies among coefficients, in which a set of hyperparameters are employed to control the sparsity of signal coefficients. Unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters of its immediate neighbors. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured-sparse solutions. The hyperparameters, along with the sparse signal, are learned by maximizing their posterior probability via an expectation-maximization (EM) algorithm. Numerical results show that the proposed algorithm presents uniform superiority over other existing methods in a series of experiments.

Relational data-like graphs, networks, and matrices-is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynamic networks. Our model contains three main components: We model the birth and death of individual groups with respect to the dynamics of the network structure via a distance dependent Indian Buffet Process. We capture the evolution of individual node group memberships via a Factorial Hidden Markov model. And, we explain the dynamics of the network structure by explicitly modeling the connectivity structure of groups. We demonstrate our model's capability of identifying the dynamics of latent groups in a number of different types of network data. Experimental results show that our model provides improved predictive performance over existing dynamic network models on future network forecasting and missing link prediction.

We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require maximizing a certain submodular function (like coverage or diversity) while simultaneously minimizing another (like cooperative cost). These problems are often posed as minimizing the difference between submodular functions [14, 37] which is in the worst case inapproximable. We show, however, that by phrasing these problems as constrained optimization, which is more natural for many applications, we achieve a number of bounded approximation guarantees. We also show that both these problems are closely related and an approximation algorithm solving one can be used to obtain an approximation guarantee for the other. We provide hardness results for both problems thus showing that our approximation factors are tight up to log-factors. Finally, we empirically demonstrate the performance and good scalability properties of our algorithms.

Human activity and environment produces sounds such as, at home, the noise produced by water, cough, or television. These sounds can be used to determine the activity in the environment. The objective is to monitor a person's activity or determine his environment using a single low cost microphone by sound analysis. The purpose is to adapt programs to the activity or environment or detect abnormal situations. Some patterns of over expressed repeatedly in the sequences of recognized sounds inter and intra environment allow to characterize activities such as the entrance of a person in the house, or a tv program watched. We first manually annotated 1500 sounds of daily life activity of old persons living at home recognized sounds. Then we inferred an ontology and enriched the database of annotation with a crowed sourced manual annotation of 7500 sounds to help with the annotation of the most frequent sounds. Using learning sound algorithms, we defined 50 types of the most frequent sounds. We used this set of recognizable sounds as a base to tag sounds and put tags on them. By using over expressed number of motifs of sequences of the tags, we were able to categorize using only a single low-cost microphone, complex activities of daily life of a persona at home as watching TV, entrance in the apartment of a person, or phone conversation including detecting unknown activities as repeated tasks performed by users.

Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms guarantee an output conductance of $\tilde{O}(\sqrt{\phi(A)})$ when the target set $A$ has conductance $\phi(A)\in[0,1]$. In this paper, we improve it to $$\tilde{O}\bigg( \min\Big\{\sqrt{\phi(A)}, \frac{\phi(A)}{\sqrt{\mathsf{Conn}(A)}} \Big\} \bigg)\enspace, $$ where the internal connectivity parameter $\mathsf{Conn}(A) \in [0,1]$ is defined as the reciprocal of the mixing time of the random walk over the induced subgraph on $A$. For instance, using $\mathsf{Conn}(A) = \Omega(\lambda(A) / \log n)$ where $\lambda$ is the second eigenvalue of the Laplacian of the induced subgraph on $A$, our conductance guarantee can be as good as $\tilde{O}(\phi(A)/\sqrt{\lambda(A)})$. This builds an interesting connection to the recent advance of the so-called improved Cheeger's Inequality [KKL+13], which says that global spectral algorithms can provide a conductance guarantee of $O(\phi_{\mathsf{opt}}/\sqrt{\lambda_3})$ instead of $O(\sqrt{\phi_{\mathsf{opt}}})$. In addition, we provide theoretical guarantee on the clustering accuracy (in terms of precision and recall) of the output set. We also prove that our analysis is tight, and perform empirical evaluation to support our theory on both synthetic and real data. It is worth noting that, our analysis outperforms prior work when the cluster is well-connected. In fact, the better it is well-connected inside, the more significant improvement (both in terms of conductance and accuracy) we can obtain. Our results shed light on why in practice some random-walk-based algorithms perform better than its previous theory, and help guide future research about local clustering.

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a third observed multinomial distribution. We study the entire relaxation path for this problem in detail. We show existence and a geometric description of the relaxation path. Specifically, we show that the maximum entropy relaxation path admits a planar geometric description as an increasing, piecewise linear function in the inverse relaxation parameter. We derive fast algorithms for tracking the path. In various realistic settings, our algorithms require $O(n\log(n))$ operations for probability distributions on $n$ points, making it possible to handle large problems. Once the path has been recovered, we show that given a validation set, the family of admissible models is reduced from an infinite family to a small, discrete set. We demonstrate the merits of our approach in experiments with synthetic data and discuss its potential for the estimation of compact n-gram language models.

Fixed and wireless networks are increasingly converging towards common connectivity with IP-based core networks. Providing effective end-to-end resource and QoS management in such complex heterogeneous converged network scenarios requires unified, adaptive and scalable solutions to integrate and co-ordinate diverse QoS mechanisms of different access technologies with IP-based QoS. Policy-Based Network Management (PBNM) is one approach that could be employed to address this challenge. Hence, a policy-based framework for end-to-end QoS management in converged networks, CNQF (Converged Networks QoS Management Framework) has been proposed within our project. In this paper, the CNQF architecture, a Java implementation of its prototype and experimental validation of key elements are discussed. We then present a fuzzy-based CNQF resource management approach and study the performance of our implementation with real traffic flows on an experimental testbed. The results demonstrate the efficacy of our resource-adaptive approach for practical PBNM systems.

This paper presents Correlated Nystrom Views (XNV), a fast semi-supervised algorithm for regression and classification. The algorithm draws on two main ideas. First, it generates two views consisting of computationally inexpensive random features. Second, XNV applies multiview regression using Canonical Correlation Analysis (CCA) on unlabeled data to bias the regression towards useful features. It has been shown that, if the views contains accurate estimators, CCA regression can substantially reduce variance with a minimal increase in bias. Random views are justified by recent theoretical and empirical work showing that regression with random features closely approximates kernel regression, implying that random views can be expected to contain accurate estimators. We show that XNV consistently outperforms a state-of-the-art algorithm for semi-supervised learning: substantially improving predictive performance and reducing the variability of performance on a wide variety of real-world datasets, whilst also reducing runtime by orders of magnitude.

We consider the problem of estimating an unknown signal $x_0$ from noisy linear observations $y = Ax_0 + z\in R^m$. In many practical instances, $x_0$ has a certain structure that can be captured by a structure inducing convex function $f(\cdot)$. For example, $\ell_1$ norm can be used to encourage a sparse solution. To estimate $x_0$ with the aid of $f(\cdot)$, we consider the well-known LASSO method and provide sharp characterization of its performance. We assume the entries of the measurement matrix $A$ and the noise vector $z$ have zero-mean normal distributions with variances $1$ and $\sigma^2$ respectively. For the LASSO estimator $x^*$, we attempt to calculate the Normalized Square Error (NSE) defined as $\frac{\|x^*-x_0\|_2^2}{\sigma^2}$ as a function of the noise level $\sigma$, the number of observations $m$ and the structure of the signal. We show that, the structure of the signal $x_0$ and choice of the function $f(\cdot)$ enter the error formulae through the summary parameters $D(cone)$ and $D(\lambda)$, which are defined as the Gaussian squared-distances to the subdifferential cone and to the $\lambda$-scaled subdifferential, respectively. The first LASSO estimator assumes a-priori knowledge of $f(x_0)$ and is given by $\arg\min_{x}\{{\|y-Ax\|_2}~\text{subject to}~f(x)\leq f(x_0)\}$. We prove that its worst case NSE is achieved when $\sigma\rightarrow 0$ and concentrates around $\frac{D(cone)}{m-D(cone)}$. Secondly, we consider $\arg\min_{x}\{\|y-Ax\|_2+\lambda f(x)\}$, for some $\lambda\geq 0$. This time the NSE formula depends on the choice of $\lambda$ and is given by $\frac{D(\lambda)}{m-D(\lambda)}$. We then establish a mapping between this and the third estimator $\arg\min_{x}\{\frac{1}{2}\|y-Ax\|_2^2+ \lambda f(x)\}$. Finally, for a number of important structured signal classes, we translate our abstract formulae to closed-form upper bounds on the NSE.